Fracture Mechanics: Integration of Mechanics, Materials Science and Chemistry

232 Pages·2010·2.42 MB·English

by  Robert P. Wei

This page intentionally left blank
FRACTURE MECHANICS
Fracture and “slow” crack growth reflect the response of a material
(i.e., its microstructure) to the conjoint actions of mechanical and
chemical driving forces and are affected by temperature. Therefore,
there is a need for quantitative understanding and modeling of the
influences of chemical and thermal environments, and of microstruc-
ture,intermsofthekeyinternalandexternalvariablesandfortheir
incorporation into design and probabilistic implications. This text,
whichtheauthorhasusedinafracturemechanicscourseforadvanced
undergraduate and graduate students, is based on the work of the
author’sLehighUniversityteamwhoseintegrativeresearchcombined
fracture mechanics, surface and electrochemistry, materials science,
andprobabilityandstatisticstoaddressarangeoffracturesafetyand
durabilityissuesonaluminum,ferrous,nickel,andtitaniumalloys,and
ceramics. Examples from this research are included to highlight the
approach and applicability of the findings in practical durability and
reliabilityproblems.
Robert P. Wei is the Reinhold Professor of Mechanical Engineering
andMechanicsatLehighUniversity.Hisprincipalresearchisinfrac-
ture mechanics, including chemical, microstructural, and mechanical
considerationsofstresscorrosioncracking,fatigue,andcorrosion,and
in life-cycle engineering. He is the author of hundreds of refereed
researchpublications.HeisaFellowoftheAmericanSocietyforTest-
ingandMaterials;theAmericanSocietyofMetalsInternational;and
theAmericanInstituteofMining,Metallurgical,andPetroleumEngi-
neering and a member of Sigma Xi and the Phi Beta Delta Interna-
tionalHonorSocieties.

Fracture Mechanics
INTEGRATION OF MECHANICS,
MATERIALS SCIENCE, AND CHEMISTRY
Robert P. Wei
LehighUniversity
CAMBRIDGE UNIVERSITY PRESS
Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore,
São Paulo, Delhi, Dubai, Tokyo
Cambridge University Press
The Edinburgh Building, Cambridge CB2 8RU, UK
Published in the United States of America by Cambridge University Press, New York
www.cambridge.org
Information on this title: www.cambridge.org/9780521194891
© Robert P. Wei 2010
This publication is in copyright. Subject to statutory exception and to the
provision of relevant collective licensing agreements, no reproduction of any part
may take place without the written permission of Cambridge University Press.
First published in print format 2010
ISBN-13 978-0-511-67699-4 eBook (NetLibrary)
ISBN-13 978-0-521-19489-1 Hardback
Cambridge University Press has no responsibility for the persistence or accuracy
of urls for external or third-party internet websites referred to in this publication,
and does not guarantee that any content on such websites is, or will remain,
accurate or appropriate.
ToLee
Forherlove,counsel,dedication,andsupport

Contents
Preface pagexiii
Acknowledgments xv
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 ContextualFramework 2
1.2 LessonsLearnedandContextualFramework 4
1.3 CrackToleranceandResidualStrength 5
1.4 CrackGrowthResistanceandSubcriticalCrackGrowth 7
1.5 ObjectiveandScopeofBook 7
references 8
2 PhysicalBasisofFractureMechanics . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.1 ClassicalTheoriesofFailure 9
2.1.1 MaximumPrincipalStress(orTresca[3])Criterion 9
2.1.2 MaximumShearingStressCriterion 10
2.1.3 MaximumPrincipalStrainCriterion 10
2.1.4 MaximumTotalStrainEnergyCriterion 10
2.1.5 MaximumDistortionEnergyCriterion 11
2.1.6 MaximumOctahedralShearingStressCriterion
(vonMises[4]Criterion) 12
2.1.7 CommentsontheClassicalTheoriesofFailure 12
2.2 FurtherConsiderationsofClassicalTheories 12
2.3 Griffith’sCrackTheoryofFractureStrength 14
2.4 ModificationstoGriffith’sTheory 16
2.5 EstimationofCrack-DrivingForceGfromEnergyLossRate
(IrwinandKies[8,9]) 17
2.6 ExperimentalDeterminationofG 20
2.7 FractureBehaviorandCrackGrowthResistanceCurve 21
references 25
vii
viii Contents
3 StressAnalysisofCracks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.1 Two-DimensionalTheoryofElasticity 26
3.1.1 Stresses 27
3.1.2 Equilibrium 27
3.1.3 Stress-StrainandStrain-DisplacementRelations 28
3.1.4 CompatibilityRelationship 29
3.2 Airy’sStressFunction 30
3.2.1 BasicFormulation 30
3.2.2 MethodofSolutionUsingFunctionsofComplexVariables 32
ComplexNumbers 32
ComplexVariablesandFunctions 32
Cauchy-RiemannConditionsandAnalyticFunctions 33
3.3 WestergaardStressFunctionApproach[8] 34
3.3.1 Stresses 34
3.3.2 Displacement(GeneralizedPlaneStress) 35
3.3.3 StressesataCrackTipandDefinitionofStressIntensity
Factor 36
3.4 StressIntensityFactors–IllustrativeExamples 38
3.4.1 CentralCrackinanInfinitePlateunderBiaxialTension
(GriffithProblem) 39
StressIntensityFactor 39
Displacements 41
3.4.2 CentralCrackinanInfinitePlateunderaPairof
ConcentratedForces[2–4] 41
3.4.3 CentralCrackinanInfinitePlateunderTwoPairsof
ConcentratedForces 43
3.4.4 CentralCrackinanInfinitePlateSubjectedtoUniformly
DistributedPressureonCrackSurfaces 43
3.5 RelationshipbetweenGandK 45
3.6 PlasticZoneCorrectionFactorandCrack-Opening
Displacement 47
PlasticZoneCorrectionFactor 47
Crack-Tip-OpeningDisplacement(CTOD) 48
3.7 ClosingComments 48
references 49
4 ExperimentalDeterminationofFractureToughness . . . . . . . . . . . . . .50
4.1 PlasticZoneandEffectofConstraint 50
4.2 EffectofThickness;PlaneStrainversusPlaneStress 52
4.3 PlaneStrainFractureToughnessTesting 54
4.3.1 FundamentalsofSpecimenDesignandTesting 55
4.3.2 PracticalSpecimensandthe“Pop-in”Concept 58
4.3.3 SummaryofSpecimenSizeRequirement 60